Interpretive Summary: The operation and design of many engineering systems are affected by an uncertain future. Decisions regarding their design, however, must be made in the present. Complicated mathematical modes can consider this type of problem, but, in the past, procedures that fully account for the uncertain future have been burdensome computationally. New mathematical procedures now allow more complex systems to be considered. This paper provides an overview of one such method known as Regularized Stochastic Decomposition (RSD) and demonstrates the method by applying it to two water resources problems with uncertain elements.

Technical Abstract:
Many engineering systems are affected by uncertainty in future demands or inputs. Decisions regarding their design, however, must be made in the present. Two-stage stochastic programming can consider this type of problem, but, in the past, procedures to fully incorporate the uncertainty have come with a high computational cost. New algorithmic developments, such as Regularized Stochastic Decomposition (RSD), now allow more complex systems to be considered. This paper provides an overview of the RSD method and its extensions and demonstrates the application of two-stage stochastic programming to two water resources problems with different problem structures and types of uncertainty.